Covariate shift relaxes the widely-employed independent and identically distributed (IID) assumption by allowing different training and testing input distributions. Unfortunately, common methods for addressing covariate shift by trying to remove the bias between training and testing distributions using importance weighting often provide poor performance guarantees in theory and unreliable predi...

In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods for the linear setting cannot be directly employed. To attack this problem, we propose estimating the distorting functions by nonparametrically regressing th...

Various methods to control the influence of a covariate on a response variable are compared. In particular, ANOVA with or without homogeneity of variances (HOV) of errors and Kruskal-Wallis (K-W) tests on covariate-adjusted residuals and analysis of covariance (ANCOVA) are compared. Covariate-adjusted residuals are obtained from the overall regression line fit to the entire data set ignoring th...

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

When a treatment influences both the primary response and the covariate, a standard analysis of covariance may misrepresent the real treatment effect by adjusting out that part of the effect which is manifest in the covariate. What parametric function should we examine if the treatments influence the covariate? An informative analysis would let the complete effects of the levels emerge, yet per...

Conclusions In the proportional hazards model the effect of a covariate is assumed to be time-invariant. In this paper a graphical method based on a linear regression model (LRM) is used to test whether this assumption is realistic. The variation in the effect of a covariate is plotted against time. The slope of this plot indicates the nature of the influence of a covariate over time. A covaria...

Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides insight into the systems that generated the graphs. Moreover, in applications such as connectomics, social networks, and genomics, graph data are accompanie...

In many learning settings, the source data available to train a regression model differs from the target data it encounters when making predictions due to input distribution shift. Appropriately dealing with this situation remains an important challenge. Existing methods attempt to “reweight” the source data samples to better represent the target domain, but this introduces strong inductive bia...

The propensity score plays a central role in a variety of causal inference settings. In particular, matching and weighting methods based on the estimated propensity score have become increasingly common in the analysis of observational data. Despite their popularity and theoretical appeal, the main practical difficulty of these methods is that the propensity score must be estimated. Researchers...